When you arrive at Route 31, you'll run into a fairly similar bunch of wild Pokemon, similar indeed to the ones you met on Route 30. Unfortunately, there's still not much of Route 31 for you to explore, which is likely why the Pokemon types found here are so similar to previous areas. You can head to the right, northward, and then to the left to fight a lone trainer.

You can also find a couple of items strewn about -- a Potion and a Poke Ball to be exact. For the time being, we'll ignore the cave entrance into the Dark Cave (we'll get there soon enough, worry not). Once you've gathered the items, fought the lone trainer, and found a way to get around the low-lying cliffs to your left (go around them via the grassy locale to the south), you'll run into a building that separates Route 31 from Violet City. Within this building, you'll be intercepted by your friend from back home once more -- this time, she'll hand over the Vs. Recorder. Then, with that in hand, you're free to continue to your left, where you'll finally reach Violet City.